Belton, A and Guillot, D and Khare, A and Putinar, M (2022) Hirschman-Widder densities. In: Applied and Computational Harmonic Analysis, 60 . pp. 396-425.
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Abstract
Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations of one-sided exponential functions. The members of this class are probability densities, and the class is closed under convolution but not under pointwise multiplication. We show that, generically, a polynomial function of such a density is a Pólya frequency function only if the polynomial is a homothety, and also identify a subclass for which each positive-integer power is a Pólya frequency function. We further demonstrate connections between the Maclaurin coefficients, the moments of these densities, and the recovery of the density from finitely many moments, via Schur polynomials. © 2022 Elsevier Inc.
| Item Type: | Journal Article |
|---|---|
| Publication: | Applied and Computational Harmonic Analysis |
| Publisher: | Academic Press Inc. |
| Additional Information: | The copyright for this article belongs to Authors |
| Keywords: | Polynomials, Hypoexponential distribution; Linear combinations; Point wise; Polya frequency; Polya frequency function; Polynomial functions; Positive integers; Probability densities; Totally positive; Totally positive function, Exponential functions |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 19 May 2022 05:27 |
| Last Modified: | 19 May 2022 05:27 |
| URI: | https://eprints.iisc.ac.in/id/eprint/71977 |
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